Question

What is $\underset{x\to 0}{lim}\frac{5^x-1}{x}$ equal to?

• A. $lo{g}_{e}5$
• B. $lo{g}_{5}e$
• C. $5$
• D. $1$

Answer 1

The correct option is A $lo{g}_{e}5$

$\underset{x\to 0}{lim}\frac{5^x-1}{x}=\frac{5^0-1}{0}\frac{0}{0}$form

$\underset{x\to 0}{lim}\frac{5^x\log 5-0}{1}=5^0\log 5=\log 5$

(or)

$\underset{x\to 0}{lim}\frac{a^x-1}{x}=\log a$